Question: Simplify; express your answer in exponential form. Assume $z\neq 0, x\neq 0$. $\dfrac{{(z^{4}x^{-3})^{2}}}{{(z^{4}x^{3})^{-4}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(z^{4}x^{-3})^{2} = (z^{4})^{2}(x^{-3})^{2}}$ On the left, we have ${z^{4}}$ to the exponent ${2}$ . Now ${4 \times 2 = 8}$ , so ${(z^{4})^{2} = z^{8}}$ Apply the ideas above to simplify the equation. $\dfrac{{(z^{4}x^{-3})^{2}}}{{(z^{4}x^{3})^{-4}}} = \dfrac{{z^{8}x^{-6}}}{{z^{-16}x^{-12}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{8}x^{-6}}}{{z^{-16}x^{-12}}} = \dfrac{{z^{8}}}{{z^{-16}}} \cdot \dfrac{{x^{-6}}}{{x^{-12}}} = z^{{8} - {(-16)}} \cdot x^{{-6} - {(-12)}} = z^{24}x^{6}$